5) Let Z be a standard normal random variable. Calculate each of the following:

a. P(Z-1)
b. P(-1.5 < Z < 1)
c. P({-2 < Z < 0} OR {1 < Z 2})
d. P({-2 < Z < 1} AND {0 < Z < 3})

Thank you so much!

2. Originally Posted by MiyuCat
5) Let Z be a standard normal random variable. Calculate each of the following:

a. P(Z-1)
b. P(-1.5 < Z < 1)
c. P({-2 < Z < 0} OR {1 < Z 2})
d. P({-2 < Z < 1} AND {0 < Z < 3})

Thank you so much!
I suggest you review this material in your classnotes and textbook. I will show the approach for (b):

Pr(-1.5 < Z < 1) = 1 - Pr(Z < -1.5) - Pr(Z > 1).

Now note that Pr(Z > 1) = 1 - Pr(Z < 1) and Pr(Z < -1.5) = Pr(Z > 1.5) = 1 - Pr(Z < 1.5) by symmetry. Now use your tables to look up the values.

3. For all of these problems use Z table - Normal Distribution

Originally Posted by MiyuCat

a. P(Z-1)
Do you mean $P(Z<-1)$ ?

Originally Posted by MiyuCat

b. P(-1.5 < Z < 1)
This one becaomes $P(Z<1)-P(Z<-1.5)$

Originally Posted by MiyuCat

c. P({-2 < Z < 0} OR {1 < Z 2})

This one makes no sense please re-post. The OR operator will indicate the whole region taken up by both inequalities.

Originally Posted by MiyuCat

d. P({-2 < Z < 1} AND {0 < Z < 3})
The AND operator will indicate the whole region shared by both inequalities.

Try $P(0

4. c. P({-2 < Z < 0} OR {1 < Z < 2})